| Title:
|
Poisson–Lie sigma models on Drinfel’d double (English) |
| Author:
|
Vysoký, Jan |
| Author:
|
Hlavatý, Ladislav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
423-447 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle.
The elegant form of equations of motion for so called Poisson-Lie groups is derived.
Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel’d double we show that Poisson-Lie group can be constructed for general Lie bialgebra. (English) |
| Keyword:
|
Poisson sigma models |
| Keyword:
|
Poisson manifolds |
| Keyword:
|
Poisson-Lie groups |
| Keyword:
|
bundle maps |
| MSC:
|
53D17 |
| MSC:
|
70G45 |
| idMR:
|
MR3007623 |
| DOI:
|
10.5817/AM2012-5-423 |
| . |
| Date available:
|
2012-12-17T14:06:51Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143116 |
| . |
| Reference:
|
[1] Bojowald, M., Kotov, A., Strobl, T.: Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries.J. Geom. Phys. 54 (2005), 400–426. Zbl 1076.53102, MR 2144710, 10.1016/j.geomphys.2004.11.002 |
| Reference:
|
[2] Calvo, I.: Poisson sigma models on surfaces with boundary: Classical and quantum aspects.Ph.D. thesis, University of Zaragoza, 2006. |
| Reference:
|
[3] Calvo, I., Falceto, F., García–Álvarez, D.: Topological Poisson sigma models on Poisson–Lie groups.JHEP, 0310 (033), 2003. MR 2030758 |
| Reference:
|
[4] Dufour, J–P., Zung, N. T.: Poisson Structures and Their Normal Forms.Progr. Math., vol. 242, Birkhäuser Verlag, 2005. Zbl 1082.53078, MR 2178041 |
| Reference:
|
[5] Klimčík, C.: Yang–Baxter $\sigma $–models and $d{S}/{A}d{S}$ T–Duality.JHEP, 0212 (051), 2002. |
| Reference:
|
[6] Klimčík, C., Ševera, P.: T–duality and the moment map.hep-th/9610198. Zbl 0924.58132 |
| Reference:
|
[7] Klimčík, C., Ševera, P.: Poisson–Lie T–duality and loops of Drinfeld doubles.Phys. Lett. B 375 (1996), 65–71. |
| Reference:
|
[8] Lu, J., Weinstein, A.: Poisson Lie groups, dressing transformations, and Bruhat decompositions.J. Differential Geom. 31 (1990), 501–526. Zbl 0673.58018, MR 1037412 |
| Reference:
|
[9] Nakahara, M.: Geometry, Topology and Physics.Taylor & Francis, 2003. Zbl 1090.53001, MR 2001829 |
| Reference:
|
[10] Schaller, P., Strobl, T.: Poisson–Sigma–Models: A generalization of 2–D gravity Yang–Mills–systems.hep-th/9411163. |
| Reference:
|
[11] Schaller, P., Strobl, T.: Poisson structure induced (topological) field theories.Mod. Phys. Lett. A9 (1994), 3129–3136. Zbl 1015.81574, MR 1303989, 10.1142/S0217732394002951 |
| Reference:
|
[12] Steenrod, N.: The Topology of Fibre Bundles.Princeton University Press, 1951. Zbl 0054.07103, MR 0039258 |
| Reference:
|
[13] Vaisman, I.: Lectures on the Geometry of Poisson Manifolds.Progr. Math., vol. 118, Birkhäuser Verlag, 2005. MR 1269545 |
| . |
